Rechargeable solid electrolyte metal-air batteries, and also fuel cells of the SOFC type, include ceramic basic elements such as a zirconium oxide-electrolyte layer and oxide ceramics as cathodes and anodes or as positive or negative electrodes. The combination of oxide ceramic electrodes and solid state electrolytes is referred to here as a so-called membrane electrode assembly (MEA) and enables the conversion of electrical energy into chemical energy and vice-versa. A redox pair of metal and metal oxide, such as, for example, iron and iron oxide in various stages of oxidation or nickel and nickel oxide, is used for storing the energy in the solid electrolyte-metal-air battery. Here the oxygen is brought from the negative electrode to the surface of the storage medium by a gaseous redox pair, in the simplest case H2/H2O. A fundamental problem of such described batteries, and also of other energy conversion cells that rely on the rather brittle oxide ceramic MEA structures, is the electrical contacting of the MEAs in each case, because the oxide ceramic electrolyte layer only has low conductivity and current carrying capacity. In addition, such MEA structures are relatively brittle, and excessive internal stresses can occur within the MEA when assembling a plurality of energy conversion cells into stacks with small manufacturing tolerances. However, the described structure can only be electrically tested regarding its electrical properties in the assembled state.